Sum of Evenly Spaced Numbers via the Middle
A run of consecutive or evenly spaced numbers adds up to the middle value times the count (or pairs with a constant sum). Children first add short runs, then generalize to long sequences and grid relations where pairing collapses a tedious sum into one product. The insight reappears as the arithmetic-series shortcut.
grade 2–4 NBTOA Look for a PatternIdentify Subproblems
Progression (5)
2-2 1. Sum a repeating number sequence 4.OA.C.53.OA.A.3
3-1 2. Sum consecutive numbers via the middle 3.OA.D.93.NBT.A.22.NBT.A.2
3-2 3. Consecutive integers around a middle value 3.OA.D.93.OA.D.8
3-2 4. Sum of evenly spaced numbers equals middle times count 3.OA.D.93.OA.C.7
4-1 5. Pair consecutive numbers with constant sum 4.OA.C.53.OA.D.9